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Free fall with initial velocity
When we now put it all together, we end up with
r
(
t
) =
r
0
+
v
0
t
-
g
t
2
/2 =
(
0
0
)
+
(
0
v
0y
)
t
-
(
0
g
)
t
2
/2
=
(
0
v
0y
t
- g
t
2
/2
)
which in components can be written as follows
x(
t
) = 0
and
y(
t
) = v
0y
t
- g
t
2
/2
Similarly, for the velocity we arrive at
v
x
(
t
) = 0
and
v
y
(
t
) = v
0y
- g
t
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